Generalized Vector-Network Formulation for the Dynamic Simulation of Multibody Systems

[+] Author and Article Information
M. J. Richard

Département de génie mécanique, Université Laval, Québec, Canada G1K 7P4

R. Anderson

Department of Mechanical Engineering, Queen’s University, Kingston, Ontario, Canada K7L 3N6

G. C. Andrews

Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

J. Dyn. Sys., Meas., Control 108(4), 322-329 (Dec 01, 1986) (8 pages) doi:10.1115/1.3143802 History: Received November 11, 1985; Online July 21, 2009


This paper describes the vector-network approach which is a comprehensive mathematical model for the systematic formulation of the nonlinear equations of motion of dynamic three-dimensional constrained multi-body systems. The entire procedure is a basic application of concepts of graph theory in which laws of vector dynamics have been combined. The main concepts of the method have been explained in previous publications but the work described herein is an appreciable extension of this relatively new approach. The method casts simultaneously the three-dimensional inertia equations associated with each rigid body and the geometrical expressions corresponding to the kinematic restrictions into a symmetrical format yielding the differential equations governing the motion of the system. The algorithm is eminently well suited for the computer-aided simulation of arbitrary interconnected rigid bodies; it serves as the basis for a “self-formulating” computer program which can simulate the response of a dynamic system, given only the system description.

Copyright © 1986 by ASME
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